Spectrum Analysis Basic Notation and Principles - Periodogram

The sine and cosine functions are mutually independent (or orthogonal); thus we may sum the squared coefficients for each frequency to obtain the periodogram. Specifically, the periodogram values above are computed as:

Pk = (sine coefficientk2 + cosine coefficientk2) * N/2

where Pk is the periodogram value at frequency νk and N is the overall length of the series. The periodogram values can be interpreted in terms of variance (sums of squares) of the data at the respective frequency or period. Customarily, the periodogram values are plotted against the frequencies or periods, and many such plots are available in the Time Series module (see the Single Series Fourier (Spectral) Analysis Results dialog).